Please refer to FIG. 1, which is a schematic diagram showing a conventional arctangent phase-discriminating (APD) device. As shown, the APD device 10 includes a local oscillator 11, two multiplication circuits 121 and 122, two integration circuit 131 and 132, and a phase-estimating unit 14. The APD device 10 receives an input signal S1 and produces an estimated phase {circumflex over (θ)}1 of the input signal S1, wherein the input signal S1 has a carrier frequency fC and a phase θ1. For instance, the input signal S1 may be expressed as {E1 cos(2pfCt+θ1)+n1(t)}, wherein E1 is the signal amplitude, n1(t) is the added Gaussian noise, and t is the time.
The local oscillator 11 produces an in-phase reference wave R1I and a quadrature reference wave R1Q. The in-phase reference wave R1I may be expressed as cos(2pfCt). The quadrature reference wave R1Q has 90° (p/2 radians) out of phase in comparison with the in-phase reference wave R1I, and may be expressed as sin(2pfCt). The multiplication circuit 121 receives the input signal S1 and the in-phase reference wave R1I, and multiplies the input signal S1 by the in-phase reference wave R1I to produce a signal SRI. The multiplication circuit 122 receives the input signal S1 and the quadrature reference wave R1Q, and multiplies the input signal S1 by the quadrature reference wave R1Q to produce a signal SRQ.
The integration circuit 131 receives the signal SRI, and integrates the signal SRI for a certain time interval to produce an in-phase component IA of the input signal S1, wherein the in-phase component IA may be an estimate of (E1 cos θ1). The integration circuit 132 receives the signal SRQ, and integrates the signal SRQ for the certain time interval to produce a quadrature component QA of the input signal S1, wherein the quadrature component QA may be an estimate of (E1 sin θ1). In a conventional scheme, the integration circuits 131 and 132 process the signals SRI and SRQ by a multiple-bit A/D conversion operation to respectively produce the in-phase component IA and the quadrature component QA.
The phase-estimating unit 14 receives the in-phase component IA and the quadrature component QA, and performs an arctangent operation tan−1(QA/IA) to produce the estimated phase {circumflex over (θ)}1.
However, the arctangent operation tan−1(QA/IA) is complex due to the nonlinear form, and thus performing the arctangent operation tan−1(QA/IA) requires heavy computation storage, additional power consumption and automatic gain control. Therefore, it is necessary to improve the disadvantages of the APD device 10.